Series: Monographs in Mathematics, Vol. 103
2011, XV, 415 p.
Hardcover, ISBN 978-3-0348-0211-6
Due: October 17, 2011
This is the second of a two volume work presenting a comprehensive exposition of extension results for maps between different geometric objects and of extension-trace results for smooth functions on subsets with no a priori differential structure (Whitney problems). The account covers the development of the area from the initial classical works of the first half of the 20th century to the flourishing period of the last decade. Seemingly very specific, these problems have been from the very beginning a powerful source of ideas, concepts and methods that essentially influenced and in some cases even transformed considerable areas of analysis. Aside from the material linked by the aforementioned problems the work is also unified by the geometric analysis approach used in the proofs of basic results. This requires a variety of geometric tools from convex and combinatorial geometry to geometry of metric space theory to Riemannian and Coarse geometry and more. The necessary facts are presented mostly with detailed proofs to make the book accessible to a wide audience.
Part 3. Lipschitz Extensions from Subsets of Metric Spaces.- Chapter 6. Extensions of Lipschitz Maps.- Chapter 7. Simultaneous Lipschitz Extensions.- Chapter 8. Linearity and Nonlinearity.- Part 4. Smooth Extension and Trace Problems for Functions on Subsets of Rn.- Chapter 9. Traces to Closed Subsets: Criteria, Applications.- Chapter 10. Whitney Problems.- Bibliography.- Index.
Series: Progress in Mathematics, Vol. 294
2012, Approx. 310 p.
Hardcover, ISBN 978-3-0348-0205-5
Due: October 2, 2011
The monograph gives a unified exposition of the thermodynamic formalism and some of its main extensions, with emphasis on the relation to the dimension theory and the multifractal analysis of dynamical systems. In particular, the book considers three different flavors of the thermodynamic formalism, namely nonadditive, subadditive, and almost additive, and provides a detailed discussion of some of the most significant results in the area, some of them quite recent. It also includes a discussion of the most substantial applications of these flavors of the thermodynamic formalism to the dimension theory and the multifractal analysis of dynamical systems. The text is self-contained.
Preface.- 1 Introduction.- I Classical Thermodynamic Formalism.- 2 Thermodynamic Formalism: Basic Notions.- 3 The Case of Symbolic Dynamics.- II Nonadditive Thermodynamic Formalism.- 4 Nonadditive Thermodynamic Formalism.- 5 Dimension Estimates for Repellers.- 6 Dimension Estimates for Hyperbolic Sets.- III Subadditive Thermodynamic Formalism.- 7 Asymptotically Subadditive Sequences.- 8 Limit Sets of Geometric Constructions.- 9 Entropy Spectra.- IV Almost Additive Thermodynamic Formalism.- 10 Almost Additive Sequences.- 11 Nonconformal Repellers.- 12 Multifractal Analysis.- Bibliography.
Published 18th May 2011 503 pages
Series: Chapman & Hall/CRC Texts in Statistical Science
An intuitive and mathematical introduction to subjective probability and Bayesian statistics.
An accessible, comprehensive guide to the theory of Bayesian statistics, Principles of Uncertainty presents the subjective Bayesian approach, which has played a pivotal role in game theory, economics, and the recent boom in Markov Chain Monte Carlo methods. Both rigorous and friendly, the book contains:
*Introductory chapters examining each new concept or assumption
*Just-in-time mathematics ? the presentation of ideas just before they are applied
*Summary and exercises at the end of each chapter
*Discussion of maximization of expected utility
*The basics of Markov Chain Monte Carlo computing techniques
*Problems involving more than one decision-maker
Written in an appealing, inviting style, and packed with interesting examples, Principles of Uncertainty introduces the most compelling parts of mathematics, computing, and philosophy as they bear on statistics. Although many books present the computation of a variety of statistics and algorithms while barely skimming the philosophical ramifications of subjective probability, this book takes a different tack. By addressing how to think about uncertainty, this book gives readers the intuition and understanding required to choose a particular method for a particular purpose.
Published 2nd June 2011 546 pages
Series: Chapman &Hall/CRC The R Series
Extensively updated to reflect the evolution of statistics and computing, the second edition of the bestselling R Graphics comes complete with with new packages and new examples. Paul Murrell, widely known as the leading expert on R graphics, has developed an in-depth resource that helps both neophyte and seasoned users master the intricacies of R graphics.
*Updated information on the core graphics engine, the traditional graphics system, the grid graphics system, and the lattice package
*A new chapter on the ggplot2 package
*New chapters on applications and extensions of R Graphics, including geographic maps, dynamic and interactive graphics, and node-and-edge graphs
Organized into five parts, R Graphics covers both "traditional" and newer, R-specific graphics systems. The book reviews the graphics facilities of the R language and describes Rfs powerful grid graphics system. The book then covers the graphics engine, which represents a common set of fundamental graphics facilities, and provides a series of brief overviews of some of the major areas of application for R graphics, and some of the major extensions of R graphics.
ICP Advanced Texts in Mathematics
264pp (approx.) Pub. date: Scheduled Winter 2011
ISBN: 978-1-84816-741-4
A central area of study in Differential Geometry is the examination of the relationship between the purely algebraic properties of the Riemann curvature tensor and the underlying geometric properties of the manifold. In this book, the findings of numerous investigations in this field of study are reviewed and presented in a clear, coherent form, including the latest developments and proofs. Even though many authors have worked in this area in recent years, many fundamental questions still remain unanswered. Many studies begin by first working purely algebraically and then later progressing onto the geometric setting and it has been found that many questions in differential geometry can be phrased as problems involving the geometric realization of curvature. Curvature decompositions are central to all investigations in this area. The authors present numerous results including the Singer?Thorpe decomposition, the Bokan decomposition, the Nikcevic decomposition, the Tricerri?Vanhecke decomposition, the Gray?Hervella decomposition and the De Smedt decomposition. They then proceed to draw appropriate geometric conclusions from these decompositions.
The book organizes, in one coherent volume, the results of research completed by many different investigators over the past 30 years. Complete proofs are given of results that are often only outlined in the original publications. Whereas the original results are usually in the positive definite (Riemannian setting), here the authors extend the results to the pseudo-Riemannian setting and then further, in a complex framework, to para-Hermitian geometry as well. In addition to that, new results are obtained as well, making this an ideal text for anyone wishing to further their knowledge of the science of curvature.
Introduction and Statement of Results
Representation Theory
Connections, Curvature, and Differential Geometry
Affine Geometry
Kahler and Para-Kahler Geometry Affine Geometry
Riemannian Geometry
Complex and Para-Complex Geometry
Hyper Complex Geometry and Other Questions
Readership: Graduate students, researchers, mathematicians and physicist interested in the study of curvature.